Research map / Learning theory and algorithms / Matrix and tensor methods
DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DAGMA instead of GOLEM | Linear SEM structure learning · ER4/SF4, Gaussian/Gumbel/exponential noise, d=100 | SHD: 70.95$\pm$26.11 -> 17.80$\pm$5.72; improvement of 74.9% | Helped |
| Use DAGMA instead of NOTEARS | Linear SEM structure learning · ER4/SF4, Gaussian/Gumbel/exponential noise, d=100 | SHD: 75.87$\pm$13.97 -> 17.80$\pm$5.72; improvement of 76.5% | Helped |
| Use DAGMA instead of GOLEM | Linear SEM structure learning · ER4/SF4, Gaussian/Gumbel/exponential noise, d=100 | Runtime (seconds): DAGMA runs 7.7 times faster | Helped |
| Use DAGMA instead of NOTEARS | Linear SEM structure learning · ER4/SF4, Gaussian/Gumbel/exponential noise, d=100 | Runtime (seconds): DAGMA runs 19.1 times faster | Helped |
| Use DAGMA instead of GOLEM | Linear SEM structure learning · ER4/SF4, Gaussian/Gumbel/exponential noise, d=20 | SHD: 4.28$\pm$1.38 -> 6.78$\pm$1.64 | Hurt |
| Replace trace-of-matrix-powers acyclicity regularizers with the log-determinant characterization | DAGMA acyclicity regularization · Cycle detection and optimization | Cycle detection: At d = 13, h_expm(W) ≈ 10^{-9} and h_poly(W) ≈ 10^{-14} | Helped |
| Replace h_expm and h_poly with the log-determinant regularizer | DAGMA acyclicity optimization · Graphs with cycles | Gradient magnitude: |∇h_poly(W)| ≤ |∇h_expm(W)| ≤ |∇hldet^s=1(W)| | Helped |
| Compute acyclicity using log-determinant instead of matrix exponential or polynomial trace | Acyclicity characterization · Randomly generated matrices | Runtime: 10x faster | Helped |
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